Normal Mixture Quasi‐maximum Likelihood Estimator for GARCH Models

Lee, Taewook; Lee, Sangyeol

doi:10.1111/j.1467-9469.2008.00624.x

Cited by 26 publications

(21 citation statements)

References 34 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…In general, the s component normal mixture distribution is not identifiable, so we need the following identification condition as in Lee and Lee (2009). DenoteΘ the set of all ϑ satisfying…”

Section: Methodology and Main Resultsmentioning

confidence: 99%

Normal mixture quasi maximum likelihood estimation for non-stationary TGARCH(1,1) models

Wang

Pan²

2014

Statistics & Probability Letters

View full text Add to dashboard Cite

This version is available at https://strathprints.strath.ac.uk/49282/ Strathprints is designed to allow users to access the research output of the University of Strathclyde. Unless otherwise explicitly stated on the manuscript, Copyright © and Moral Rights for the papers on this site are retained by the individual authors and/or other copyright owners. Please check the manuscript for details of any other licences that may have been applied. You may not engage in further distribution of the material for any profitmaking activities or any commercial gain. You may freely distribute both the url (https://strathprints.strath.ac.uk/) and the content of this paper for research or private study, educational, or not-for-profit purposes without prior permission or charge.Any correspondence concerning this service should be sent to the Strathprints administrator: strathprints@strath.ac.ukThe Strathprints institutional repository (https://strathprints.strath.ac.uk) is a digital archive of University of Strathclyde research outputs. It has been developed to disseminate open access research outputs, expose data about those outputs, and enable the management and persistent access to Strathclyde's intellectual output. Normal Mixture Quasi Maximum Likelihood Estimation forNon-Stationary TGARCH(1, 1) ModelsHui Wang 1 and Jiazhu Pan 2 * 1 School of Finance, Central University of Finance and Economics, China.2 Department of Mathematics and Statistics, University of Strathclyde, UK .Abstract: Although quasi maximum likelihood estimator based on Gaussian density (G-QMLE) is widely used to estimate GARCH-type models, it does not perform successfully when error distribution is either skewed or leptokurtic. This paper proposes normal mixture quasi-maximum likelihood estimator (NM-QMLE) for non-stationary TGARCH(1, 1) models. We show that, under mild regular conditions, there is no consistent estimator for the intercept, and the proposed estimator for any other parameter is consistent.

show abstract

Section: Methodology and Main Resultsmentioning

confidence: 99%

Normal mixture quasi maximum likelihood estimation for non-stationary TGARCH(1,1) models

Wang

Pan²

2014

Statistics & Probability Letters

View full text Add to dashboard Cite

show abstract

“…Mikosch and Stărică (2000)). Knowledge about the normal assumption concerning GARCH innovations is very useful since in case the normality assumption is violated, it is desirable to adopt a newly developed parameter estimation procedure as proposed by Berkes and Horváth (2004) and Lee and Lee (2009) rather than the Gaussian QMLE (quasi maximum likelihood estimation) method proposed by Francq and Zakoïan (2004).…”

Section: Introductionmentioning

confidence: 99%

A note on the Jarque–Bera normality test for GARCH innovations

Lee

Park

Lee

2010

Journal of the Korean Statistical Society

Self Cite

View full text Add to dashboard Cite

a b s t r a c tIn this paper, we consider the validity of the Jarque-Bera normality test whose construction is based on the residuals, for the innovations of GARCH (generalized autoregressive conditional heteroscedastic) models. It is shown that the asymptotic behavior of the original form of the JB test adopted in this paper is identical to that of the test statistic based on true errors. The simulation study also confirms the validity of the original form since it outperforms other available normality tests.

show abstract

“…Asymptotic theory of the quasi-maximum likelihood estimator(QMLE) in GARCH context were first established by Weiss (1986) for ARCH model, and followed by Lumsdaine (1996) for GARCH(1, 1) processes. Further studies for general GARCH(p, q) models can be found in Berkes et al (2003), Straumann and Mikosch (2006) and Lee and Lee (2009). We refer to Straumann (2005) for a recent comprehensive treatment on the estimation of GARCH models in a broader context.…”

Section: Introductionmentioning

confidence: 99%

Asymptotic Normality for Threshold-Asymmetric GARCH Processes of Non-Stationary Cases

Park¹,

Hwang²

2011

Communications for Statistical Applications and Methods

View full text Add to dashboard Cite

This article is concerned with a class of threshold-asymmetric GARCH models both for stationary case and for non-stationary case. We investigate large sample properties of estimators from QML(quasi-maximum likelihood) and QL(quasilikelihood) methods. Asymptotic distributions are derived and it is interesting to note for non-stationary case that both QML and QL give asymptotic normal distributions.

show abstract

Normal Mixture Quasi‐maximum Likelihood Estimator for GARCH Models

Cited by 26 publications

References 34 publications

Normal mixture quasi maximum likelihood estimation for non-stationary TGARCH(1,1) models

Normal mixture quasi maximum likelihood estimation for non-stationary TGARCH(1,1) models

A note on the Jarque–Bera normality test for GARCH innovations

Asymptotic Normality for Threshold-Asymmetric GARCH Processes of Non-Stationary Cases

Contact Info

Product

Resources

About